The Cuntz Comparison in the Standard C*-Algebra

الملخص EN

The Cuntz comparison, introduced by Cuntz in early 1978, associates each C*-algebra with an abelian semigroup which is an invariant for the classification of the nuclear C*-algebras and called the Cuntz semigroup.

In this paper, we study the Cuntz comparison in the standard C*-algebra.

We characterize the Cuntz comparison in terms of the dimension of the operator range.

Also, we consider the structure of the semilinear map which preserves the Cuntz comparison.